Not every scholar agrees (as if!), but some identify the following structure in Matthew’s Gospel:
First Major Discourse: the Sermon on the Mount (5:1-7:28)
Parallel to: Genesis
Sandwiched by: Jesus heals the sick (4:23-25) and Jesus cleanses a leper (8:1-4)
Second Major Discourse: the Sermon on Discipleship (10:5-11:1)
Parallel to: Exodus
Sandwiched by: the Twelve commissioned (10:1-4) and John the Baptist (11:2-6)
Third Major Discourse: Parables of the Kingdom (13:1-13:53)
Parallel to: Leviticus
Sandwiched by: Jesus’ True Family (12:46-50) and Rejected because of His Family (13:54-58)
Fourth Major Discourse: How to Treat Others (18:1-19:1)
Parallel to: Numbers
Sandwiched by: Jesus Challenged: temple tax (17:24-27) and Jesus Challenged: divorce (19:2-9)
Fifth Major Discourse: Discipleship in the Last Days (24:3-26:1)
Parallel to: Deuteronomy
Sandwiched by: Temple Destroyed (23:37-24:2) and Murder Conspiracy (26:2-5)
Note that each of the five sections ends with similar phrases along the lines of “and it came to pass then when Jesus had made an end of speaking” (see 7:28, 11:1, 13:53, 19:1, and 26:1).
Each section is paralleled with one of (what are traditionally called) the books of Moses. It is generally recognized that Matthew is most concerned of the gospels with placing Jesus in a Jewish context and showing him as the fulfillment of OT prophecies. Paralleling Jesus’ main speeches with Moses’ main writings would continue that theme.
Each section consists of a major speech that is “sandwiched” by two stories that share themes (i.e., not only do the stories share themes with each other, but also with the speech that they sandwich).
This proposed structure is not without criticism since (1) you have to read the infancy and the Resurrection as ‘preamble’ and ‘epilogue’ to Jesus’ life story and (2) it is forced because chapter 23 is not really the same discourse as chapters 24-25 (see 24:1). So I’m open to the possibility that this is not the best way to read Matthew.
Nevertheless, some interesting things emerge when you approach Matthew through this lens. One is that Matthew 13, the parables of the kingdom, are supposed to be read alongside of Leviticus. This makes perfect sense in that both Leviticus and the parables need to be read analogically (more on that idea here if you are unfamiliar with it). Another benefit is, as a quick scan of the sandwiching stories and speeches will show you, that the speeches are illustrated by the stories and the points of the stories are illustrated by the speeches. For example, talk of destroying the temple is paralleled with the plan to kill Jesus, and both of the those stories relate to the challenges of being a disciple in the end times. All of that material is meant to be read in light of Deuteronomy, Moses’ final speech. It is a nice fit, and while it is true that Mt 23 and Mt 24-25 aren’t the same speech, we may not need to be too dogmatic on that point.
This structure also does my very favorite thing: it opens up lots of interesting questions to ponder. For starters: What do you learn when you read the Sermon on the Mount in light of Genesis and vice versa? What do the Parables of the Kingdom have to do with Jesus’ family? Why would healings be related to the Sermon on the Mount?
And many more.